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Re: Lunars: series vs. triangle methods
From: Fred Hebard
Date: 2004 Sep 26, 22:00 -0400
From: Fred Hebard
Date: 2004 Sep 26, 22:00 -0400
Frank, I didn't mean to be poking any sticks at you in my post, and considered putting in a disclaimer to that effect, and I recognize that approximate methods can be as accurate as "exact" methods, but I see no need to change well-established terminology in this field. As I recall, the phrase "approximation" is used almost invariably when series expansions, etc, are used to simplify equations; if nothing more, they remind us that the approximate methods might not work in all situations. I also recognize that an understanding of the terms in an approximate method can give one a better understanding of the physics. I was merely trying to point out the distinction between the two methods and to point out one advantage of the exact method for those of us who are not as mathematically proficient as you. I remember acquiring a TI-35 or TI-48 (can't remember the number) programmable calculator in 1978 or so and programming in Taylor Series expressions for sine, etc, just to see them in action and to try to infer how many terms were in the calculator's series for sine. So I know about Taylor Series and what they're used for. But it would not be a simple matter for me to derive an approximate method for solving a spherical trig problem, whereas it is for you. I suppose I could do it, but it would take me several days. I expect it also would take me quite some time to even do that Taylor Series for sine in the TI-35. Thus, for me to understand the basic spherical trig problem, the approximate method gives me little guidance, while the exact method gives quite a bit more. I also think it is wholly true that the approximate methods were developed to ease the computational burdens imposed by the exact methods. Can you offer any other reason why the approximate methods were developed and published? I might add that I don't regret that my post stimulated you to educate us more thoroughly. But my apologies if it offended you. Fred